$A$ $B$ $C$ If: $ AC = 121$, $ AB = 8x + 4$, and $ BC = 4x + 9$, Find $BC$.
From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {8x + 4} + {4x + 9} = {121}$ Combine like terms: $ 12x + 13 = {121}$ Subtract $13$ from both sides: $ 12x = 108$ Divide both sides by $12$ to find $x$ $ x = 9$ Substitute $9$ for $x$ in the expression that was given for $BC$ $ BC = 4({9}) + 9$ Simplify: $ {BC = 36 + 9}$ Simplify to find ${BC}$ : $ {BC = 45}$